Abstract

The ballistic perforation of sandwich plates comprising two identical/unidentical aluminum alloy face sheets and an aluminum foam core is investigated to gain insights into the factors governing the penetration processes. The impact velocities of projectiles with conical, flat, and hemispherical noses range from 60 ms−1 to 220 ms−1 in the experiments. Against conical-ended projectiles, petalling failure is found to be an active failure mode at the rear face sheet. Against projectiles with flat and hemispherical noses, both petalling failure and petalling-flipped-cover failure are observed. Finite element simulations considering the effect of foam meso-structure on the ballistic limit of sandwich plates are performed and validated against the experimental results. It is shown that the local bending and fracture of the cell walls significantly dissipate the kinetic energy of the projectile and restrain the occurrence of the high stress regions. Characteristic double-peak and single-peak modes of contact force time histories are observed for projectiles with various nose shapes. It is also found that a sandwich plate with thicker front face sheet has higher ballistic resistance, which may facilitate the instructional arrangement of face sheets with regard to mass distribution to achieve higher ballistic resistance. Finally, a three-stage theoretical model based on energy balance principle is developed for each type of projectile to predict the residual velocities after perforation of sandwich plate.

References

1.
Qin
,
Q. H.
, and
Wang
,
T. J.
,
2011
, “
Low-Velocity Heavy-Mass Impact Response of Slender Metal Foam Core Sandwich Beam
,”
Compos. Struct.
,
93
(
6
), pp.
1526
1537
.
2.
Hassan
,
M. Z.
,
Guan
,
Z. W.
,
Cantwell
,
W. J.
,
Langdon
,
G. S.
, and
Nurick
,
G. N.
,
2012
, “
The Influence of Core Density on the Blast Resistance of Foam-Based Sandwich Structures
,”
Int. J. Impact Eng.
,
50
, pp.
9
16
.
3.
Zhu
,
Y.
, and
Sun
,
Y.
,
2021
, “
Low-Velocity Impact Response of Multilayer Foam Core Sandwich Panels With Composite Face Sheets
,”
Int. J. Mech. Sci.
,
209
, p.
106704
.
4.
Wang
,
T.
,
Qin
,
Q.
,
Wang
,
M.
,
Yu
,
W.
,
Wang
,
J.
,
Zhang
,
J.
, and
Wang
,
T. J.
,
2017
, “
Blast Response of Geometrically Asymmetric Metal Honeycomb Sandwich Plate: Experimental and Theoretical Investigations
,”
Int. J. Impact Eng.
,
105
, pp.
24
38
.
5.
Audibert
,
C.
,
Andréani
,
A.-S.
,
Lainé
,
É.
, and
Grandidier
,
J.-C.
,
2019
, “
Discrete Modelling of Low-Velocity Impact on Nomex® Honeycomb Sandwich Structures With CFRP Skins
,”
Compos. Struct.
,
207
, pp.
108
118
.
6.
Zhang
,
X.
,
Xu
,
F.
,
Zang
,
Y.
, and
Feng
,
W.
,
2020
, “
Experimental and Numerical Investigation on Damage Behavior of Honeycomb Sandwich Panel Subjected to Low-Velocity Impact
,”
Compos. Struct.
,
236
, p.
111882
.
7.
Evans
,
A. G.
,
He
,
M. Y.
,
Deshpande
,
V. S.
,
Hutchinson
,
J. W.
,
Jacobsen
,
A. J.
, and
Carter
,
W. B.
,
2010
, “
Concepts for Enhanced Energy Absorption Using Hollow Micro-Lattices
,”
Int. J. Impact Eng.
,
37
(
9
), pp.
947
959
.
8.
Xiong
,
J.
,
Vaziri
,
A.
,
Ma
,
L.
,
Papadopoulos
,
J.
, and
Wu
,
L.
,
2012
, “
Compression and Impact Testing of Two-Layer Composite Pyramidal-Core Sandwich Panels
,”
Compos. Struct.
,
94
(
2
), pp.
793
801
.
9.
Jin
,
X.
,
Wang
,
Z.
,
Ning
,
J.
,
Xiao
,
G.
,
Liu
,
E.
, and
Shu
,
X.
,
2016
, “
Dynamic Response of Sandwich Structures With Graded Auxetic Honeycomb Cores Under Blast Loading
,”
Composites Part B
,
106
, pp.
206
217
.
10.
Beharic
,
A.
,
Rodriguez Egui
,
R.
, and
Yang
,
L.
,
2018
, “
Drop-Weight Impact Characteristics of Additively Manufactured Sandwich Structures With Different Cellular Designs
,”
Mater. Des.
,
145
, pp.
122
134
.
11.
Lan
,
X.
,
Feng
,
S.
,
Huang
,
Q.
, and
Zhou
,
T.
,
2019
, “
A Comparative Study of Blast Resistance of Cylindrical Sandwich Panels With Aluminum Foam and Auxetic Honeycomb Cores
,”
Aerosp. Sci. Technol.
,
87
, pp.
37
47
.
12.
Usta
,
F.
,
Türkmen
,
H. S.
, and
Scarpa
,
F.
,
2021
, “
Low-Velocity Impact Resistance of Composite Sandwich Panels With Various Types of Auxetic and Non-auxetic Core Structures
,”
Thin Walled Struct.
,
163
, p.
107738
.
13.
Heimbs
,
S.
,
Cichosz
,
J.
,
Klaus
,
M.
,
Kilchert
,
S.
, and
Johnson
,
A. F.
,
2010
, “
Sandwich Structures With Textile-Reinforced Composite Foldcores Under Impact Loads
,”
Compos. Struct.
,
92
(
6
), pp.
1485
1497
.
14.
Zhang
,
J.
,
Lu
,
G.
,
Zhang
,
Y.
, and
You
,
Z.
,
2021
, “
A Study on Ballistic Performance of Origami Sandwich Panels
,”
Int. J. Impact Eng.
,
156
, p.
103925
.
15.
Gibson
,
L. J.
, and
Ashby
,
M. F.
,
1997
,
Cellular Solids: Structure and Properties
, 2nd ed.,
Cambridge University Press
,
Cambridge, UK
.
16.
Reddy
,
T. Y.
,
Wen
,
H. M.
,
Reid
,
S. R.
, and
Soden
,
P. D.
,
1998
, “
Penetration and Perforation of Composite Sandwich Panels by Hemispherical and Conical Projectiles
,”
ASME J. Pressure Vessel Technol.
,
120
(
2
), pp.
186
194
.
17.
Wen
,
H. M.
,
Reddy
,
T. Y.
,
Reid
,
S. R.
, and
Soden
,
P. D.
,
1998
, “
Indentation, Penetration and Perforation of Composite Laminates and Sandwich Panels Under Quasi-Static and Projectile Loading
,”
Key Eng. Mater.
,
141
, pp.
501
552
.
18.
Gama
,
B. A.
,
Bogetti
,
T. A.
,
Fink
,
B. K.
,
Yu
,
C. J.
,
Claar
,
T. D.
,
Eifert
,
H. H.
, and
Gillespie
,
J. W.
,
2001
, “
Aluminum Foam Integral Armor: A New Dimension in Armor Design
,”
Compos. Struct.
,
52
(
3–4
), pp.
381
395
.
19.
Skvortsov
,
V.
,
Kepler
,
J.
, and
Bozhevolnaya
,
E.
,
2003
, “
Energy Partition for Ballistic Penetration of Sandwich Panels
,”
Int. J. Impact Eng.
,
28
(
7
), pp.
697
716
.
20.
Kepler
,
J.
,
2004
, “
Impact Penetration of Sandwich Panels at Different Velocities—An Experimental Parameter Study: Part I—Parameters and Results
,”
J. Sandwich Struct. Mater.
,
6
(
4
), pp.
357
374
.
21.
Kepler
,
J.
,
2004
, “
Impact Penetration of Sandwich Panels at Different Velocities—An Experimental Parameter Study: Part II—Interpretation of Results and Modeling
,”
J. Sandwich Struct. Mater.
,
6
(
5
), pp.
379
397
.
22.
Aktay
,
L.
,
Johnson
,
A. F.
, and
Holzapfel
,
M.
,
2005
, “
Prediction of Impact Damage on Sandwich Composite Panels
,”
Comput. Mater. Sci.
,
32
(
3–4
), pp.
252
260
.
23.
Velmurugan
,
R.
,
Babu
,
M. G.
, and
Gupta
,
N. K.
,
2006
, “
Projectile Impact on Sandwich Panels
,”
Int. J. Crashworthiness
,
11
(
2
), pp.
153
164
.
24.
Hou
,
W. H.
,
Zhu
,
F.
,
Lu
,
G. X.
, and
Fang
,
D. N.
,
2010
, “
Ballistic Impact Experiments of Metallic Sandwich Panels With Aluminium Foam Core
,”
Int. J. Impact Eng.
,
37
(
10
), pp.
1045
1055
.
25.
Buitrago
,
B. L.
,
Garcia-Castillo
,
S. K.
, and
Barbero
,
E.
,
2010
, “
Experimental Analysis of Perforation of Glass/Polyester Structures Subjected to High-Velocity Impact
,”
Mater. Lett.
,
64
(
9
), pp.
1052
1054
.
26.
Fatt
,
M. S. H.
, and
Sirivolu
,
D.
,
2010
, “
A Wave Propagation Model for the High Velocity Impact Response of a Composite Sandwich Panel
,”
Int. J. Impact Eng.
,
37
(
2
), pp.
117
130
.
27.
Odacı
,
İ. K.
,
Kılıçaslan
,
C.
,
Taşdemirci
,
A.
, and
Güden
,
M.
,
2012
, “
Projectile Impact Testing of Glass Fiber-Reinforced Composite and Layered Corrugated Aluminium and Aluminium Foam Core Sandwich Panels: A Comparative Study
,”
Int. J. Crashworthiness
,
17
(
5
), pp.
508
518
.
28.
Zhou
,
J.
,
Guan
,
Z.
, and
Cantwell
,
W.
,
2012
, “
The Perforation Resistance of Sandwich Structures Subjected to Low Velocity Projectile Impact Loading
,”
Aeronaut. J.
,
116
(
1186
), pp.
1247
1262
.
29.
Hassan
,
M. Z.
, and
Cantwell
,
W. J.
,
2012
, “
The Influence of Core Properties on the Perforation Resistance of Sandwich Structures—An Experimental Study
,”
Composites Part B
,
43
(
8
), pp.
3231
3238
.
30.
Zhou
,
J.
,
Guan
,
Z. W.
, and
Cantwell
,
W. J.
,
2013
, “
The Impact Response of Graded Foam Sandwich Structures
,”
Compos. Struct.
,
97
, pp.
370
377
.
31.
Nasirzadeh
,
R.
, and
Saber
,
A. R.
,
2014
, “
Study of Foam Density Variations in Composite Sandwich Panels Under High Velocity Impact Loading
,”
Int. J. Impact Eng.
,
63
, pp.
129
139
.
32.
Chen
,
P.
,
Niu
,
W.
,
Yan
,
X.
, and
Lu
,
G.
,
2016
, “
Theoretical Model for Dynamic Response of Aluminum Foam Sandwich Targets by Truncated Cone-Nosed Projectiles
,”
J. Sandwich Struct. Mater.
,
20
(
2
), pp.
249
267
.
33.
Bull
,
P. H.
, and
Hallstrom
,
S.
,
2016
, “
High-Velocity and Quasi-Static Impact of Large Sandwich Panels
,”
J. Sandwich Struct. Mater.
,
6
(
2
), pp.
97
113
.
34.
Kepler
,
J. A.
, and
Hansen
,
M. R.
,
2016
, “
Numerical Modeling of Sandwich Panel Response to Ballistic Loading—Energy Balance for Varying Impactor Geometries
,”
J. Sandwich Struct. Mater.
,
9
(
6
), pp.
553
570
.
35.
Voillat
,
R.
,
Gallien
,
F.
,
Mortensen
,
A.
, and
Gass
,
V.
,
2018
, “
Hypervelocity Impact Testing on Stochastic and Structured Open Porosity Cast Al–Si Cellular Structures for Space Applications
,”
Int. J. Impact Eng.
,
120
, pp.
126
137
.
36.
Nia
,
A. A.
, and
Kazemi
,
M.
,
2018
, “
Experimental Study of Ballistic Resistance of Sandwich Targets With Aluminum Face-Sheet and Graded Foam Core
,”
J. Sandwich Struct. Mater.
,
22
(
2
), pp.
461
479
.
37.
Cui
,
J.
,
Ye
,
R. C.
,
Zhao
,
N.
,
Wu
,
J.
, and
Wang
,
M. H.
,
2018
, “
Assessment on Energy Absorption of Double Layered and Sandwich Plates Under Ballistic Impact
,”
Thin Walled Struct.
,
130
, pp.
520
534
.
38.
Kaboglu
,
C.
,
Yu
,
L.
,
Mohagheghian
,
I.
,
Blackman
,
B. R. K.
,
Kinloch
,
A. J.
, and
Dear
,
J. P.
,
2018
, “
Effects of the Core Density on the Quasi-Static Flexural and Ballistic Performance of Fibre-Composite Skin/Foam-Core Sandwich Structures
,”
J. Mater. Sci.
,
53
(
24
), pp.
16393
16414
.
39.
Tang
,
E.
,
Zhang
,
X.
, and
Han
,
Y.
,
2019
, “
Experimental Research on Damage Characteristics of CFRP/Aluminum Foam Sandwich Structure Subjected to High Velocity Impact
,”
J. Mater. Res. Technol.
,
8
(
5
), pp.
4620
4630
.
40.
Zhao
,
N.
,
Ye
,
R.
,
Tian
,
A.
,
Cui
,
J.
,
Ren
,
P.
, and
Wang
,
M.
,
2019
, “
Experimental and Numerical Investigation on the Anti-Penetration Performance of Metallic Sandwich Plates for Marine Applications
,”
J. Sandwich Struct. Mater.
,
22
(
2
), pp.
494
522
.
41.
Ahmadi
,
H.
, and
Liaghat
,
G.
,
2019
, “
Analytical and Experimental Investigation of High Velocity Impact on Foam Core Sandwich Panel
,”
Polym. Compos.
,
40
(
6
), pp.
2258
2272
.
42.
Khaire
,
N.
,
Bhure
,
V.
, and
Tiwari
,
G.
,
2020
, “
Finite Element Analysis of Impact Response of Foams in Sandwich Panels
,”
Mater. Today: Proc.
,
28
(
4
), pp.
2585
2590
.
43.
Wu
,
Q.
,
Yang
,
C.
,
Ohrndorf
,
A.
,
Christ
,
H. J.
,
Han
,
J.
, and
Xiong
,
J.
,
2020
, “
Impact Behaviors of Human Skull Sandwich Cellular Bones: Theoretical Models and Simulation
,”
J. Mech. Behav. Biomed. Mater.
,
104
, p.
103669
.
44.
Vinson
,
J. R.
,
2001
, “
Sandwich Structures
,”
Appl. Mech. Rev.
,
54
(
3
), pp.
201
214
.
45.
Qin
,
Q.
,
Zhang
,
J.
,
Wang
,
Z.
, and
Wang
,
T. J.
,
2011
, “
Large Deflection of Geometrically Asymmetric Metal Foam Core Sandwich Beam Transversely Loaded by a Flat Punch
,”
Int. J. Aerosp. Lightweight Struct.
,
1
(
1
), p.
1650001
.
46.
Zhang
,
J.
,
Qin
,
Q.
,
Xiang
,
C.
,
Wang
,
Z.
, and
Wang
,
T. J.
,
2016
, “
A Theoretical Study of Low-Velocity Impact of Geometrically Asymmetric Sandwich Beams
,”
Int. J. Impact Eng.
,
96
, pp.
35
49
.
47.
Wang
,
Z.
,
Qin
,
Q.
,
Zhang
,
J.
, and
Wang
,
T. J.
,
2013
, “
Low-Velocity Impact Response of Geometrically Asymmetric Slender Sandwich Beams With Metal Foam Core
,”
Compos. Struct.
,
98
, pp.
1
14
.
48.
Liu
,
Q. Q.
,
Wang
,
S. P.
,
Lin
,
X.
,
Cui
,
P.
, and
Zhang
,
S.
,
2020
, “
Numerical Simulation on the Anti-Penetration Performance of Polyurea-Core Weldox 460 E Steel Sandwich Plates
,”
Compos. Struct.
,
236
, p.
111852
.
49.
Garcia-Avila
,
M.
,
Portanova
,
M.
, and
Rabiei
,
A.
,
2015
, “
Ballistic Performance of Composite Metal Foams
,”
Compos. Struct.
,
125
, pp.
202
211
.
50.
Babakhani
,
A.
,
Golestanipour
,
M.
, and
Zebarjad
,
S. M.
,
2015
, “
Modelling of Aluminium Foam Core Sandwich Panels Under Impact Perforation
,”
Mater. Sci. Technol.
,
32
(
13
), pp.
1330
1337
.
51.
Ivanez
,
I.
,
Santiuste
,
C.
,
Barbero
,
E.
, and
Sanchez-Saez
,
S.
,
2011
, “
Numerical Modelling of Foam-Cored Sandwich Plates Under High-Velocity Impact
,”
Compos. Struct.
,
93
(
9
), pp.
2392
2399
.
52.
Jing
,
L.
,
Yang
,
F.
, and
Zhao
,
L. M.
,
2017
, “
Perforation Resistance of Sandwich Panels With Layered Gradient Metallic Foam Cores
,”
Compos. Struct.
,
171
, pp.
217
226
.
53.
Tan
,
P. J.
,
Reid
,
S. R.
,
Harrigan
,
J. J.
,
Zou
,
Z.
, and
Li
,
S.
,
2005
, “
Dynamic Compressive Strength Properties of Aluminium Foams. Part I—Experimental Data and Observations
,”
J. Mech. Phys. Solids
,
53
(
10
), pp.
2174
2205
.
54.
Su
,
X.
,
Yu
,
T.
, and
Reid
,
S.
,
1995
, “
Inertia-Sensitive Impact Energy-Absorbing Structures Part I: Effects of Inertia and Elasticity
,”
Int. J. Impact Eng.
,
16
(
4
), pp.
651
672
.
55.
Su
,
X.
,
Yu
,
T.
, and
Reid
,
S.
,
1995
, “
Inertia-Sensitive Impact Energy-Absorbing Structures Part II: Effect of Strain Rate
,”
Int. J. Impact Eng.
,
16
(
4
), pp.
673
689
.
56.
Vesenjak
,
M.
,
Veyhl
,
C.
, and
Fiedler
,
T.
,
2012
, “
Analysis of Anisotropy and Strain Rate Sensitivity of Open-Cell Metal Foam
,”
Mater. Sci. Eng. A
,
541
, pp.
105
109
.
57.
Sugimura
,
Y.
,
Meyer
,
J.
,
He
,
M. Y.
,
BartSmith
,
H.
,
Grenstedt
,
J.
, and
Evans
,
A. G.
,
1997
, “
On the Mechanical Performance of Closed Cell Al Alloy Foams
,”
Acta Mater.
,
45
(
12
), pp.
5245
5259
.
58.
Evans
,
A. G.
,
Hutchinson
,
J. W.
, and
Ashby
,
M. F.
,
1998
, “
Multifunctionality of Cellular Metal Systems
,”
Prog. Mater. Sci.
,
43
(
3
), pp.
171
221
.
59.
Gioux
,
G.
,
McCormack
,
T. M.
, and
Gibson
,
L. J.
,
2000
, “
Failure of Aluminum Foams Under Multiaxial Loads
,”
Int. J. Mech. Sci.
,
42
(
6
), pp.
1097
1117
.
60.
Nieh
,
T. G.
,
Kinney
,
J. H.
,
Wadsworth
,
J.
, and
Ladd
,
A. J. C.
,
1998
, “
Morphology and Elastic Properties of Aluminum Foams Produced by a Casting Technique
,”
Scr. Mater.
,
38
(
10
), pp.
1487
1494
.
61.
Brydon
,
A. D.
,
Bardenhagen
,
S. G.
,
Miller
,
E. A.
, and
Seidler
,
G. T.
,
2005
, “
Simulation of the Densification of Real Open-Celled Foam Microstructures
,”
J. Mech. Phys. Solids
,
53
(
12
), pp.
2638
2660
.
62.
Zhang
,
J.
,
Zhao
,
G. P.
,
Lu
,
T. J.
, and
He
,
S. Y.
,
2015
, “
Strain Rate Behavior of Closed-Cell Al–Si–Ti Foams: Experiment and Numerical Modeling
,”
Mech. Adv. Mater. Struct.
,
22
(
7
), pp.
556
563
.
63.
Kinney
,
J.
,
Marshall
,
G.
,
Marshall
,
S.
, and
Haupt
,
D.
,
2001
, “
Three-Dimensional Imaging of Large Compressive Deformations in Elastomeric Foams
,”
J. Appl. Polym. Sci.
,
80
(
10
), pp.
1746
1755
.
64.
Elmoutaouakkil
,
A.
,
Fuchs
,
G.
,
Bergounhon
,
P.
,
Peres
,
R.
, and
Peyrin
,
F.
,
2003
, “
Three-Dimensional Quantitative Analysis of Polymer Foams From Synchrotron Radiation X-Ray Microtomography
,”
J. Phys. D: Appl. Phys.
,
36
(
10a
), pp.
A37
A43
.
65.
Daphalapurkar
,
N. P.
,
Hanan
,
J. C.
,
Phelps
,
N. B.
,
Bale
,
H.
, and
Lu
,
H.
,
2008
, “
Tomography and Simulation of Microstructure Evolution of a Closed-Cell Polymer Foam in Compression
,”
Mech. Adv. Mater. Struct.
,
15
(
8
), pp.
594
611
.
66.
Wismans
,
J.
,
Govaert
,
L.
, and
Van Dommelen
,
J.
,
2010
, “
X-Ray Computed Tomography-Based Modeling of Polymeric Foams: The Effect of Finite Element Model Size on the Large Strain Response
,”
J. Polym. Sci. Part B: Polym. Phys.
,
48
(
13
), pp.
1526
1534
.
67.
Kader
,
M. A.
,
Islam
,
M. A.
,
Hazell
,
P. J.
,
Escobedo
,
J. P.
,
Saadatfar
,
M.
,
Brown
,
A. D.
, and
Appleby-Thomas
,
G. J.
,
2016
, “
Modelling and Characterization of Cell Collapse in Aluminium Foams During Dynamic Loading
,”
Int. J. Impact Eng.
,
96
, pp.
78
88
.
68.
Jeon
,
I.
,
Asahina
,
T.
,
Kang
,
K. J.
,
Im
,
S.
, and
Lu
,
T. J.
,
2010
, “
Finite Element Simulation of the Plastic Collapse of Closed-Cell Aluminum Foams With X-Ray Computed Tomography
,”
Mech. Mater.
,
42
(
3
), pp.
227
236
.
69.
Youssef
,
S.
,
Maire
,
E.
, and
Gaertner
,
R.
,
2005
, “
Finite Element Modelling of the Actual Structure of Cellular Materials Determined by X-Ray Tomography
,”
Acta Mater.
,
53
(
3
), pp.
719
730
.
70.
Chen
,
Y. M.
,
Das
,
R.
, and
Battley
,
M.
,
2017
, “
Finite Element Analysis of the Compressive and Shear Responses of Structural Foams Using Computed Tomography
,”
Compos. Struct.
,
159
, pp.
784
799
.
71.
Hangai
,
Y.
,
Yamaguchi
,
R.
,
Takahashi
,
S.
,
Utsunomiya
,
T.
,
Kuwazuru
,
O.
, and
Yoshikawa
,
N.
,
2012
, “
Deformation Behavior Estimation of Aluminum Foam by X-Ray CT Image-Based Finite Element Analysis
,”
Metall. Mater. Trans. A
,
44
(
4
), pp.
1880
1886
.
72.
Toda
,
H.
,
Takata
,
M.
,
Ohgaki
,
T.
,
Kobayashi
,
M.
,
Kobayashi
,
T.
,
Uesugi
,
K.
,
Makii
,
K.
, and
Aruga
,
Y.
,
2006
, “
3-D Image-Based Mechanical Simulation of Aluminium Foams: Effects of Internal Microstructure
,”
Adv. Eng. Mater.
,
8
(
6
), pp.
459
467
.
73.
Bishop
,
R. F.
, and
Mott
,
N. F.
,
1945
, “
The Theory of Indentation and Hardness Tests
,”
Proc. Phys. Soc. Lond.
,
57
(
321
), pp.
147
159
.
74.
Chen
,
Y. L.
, and
Chen
,
H. C.
,
2012
, “
Penetration Depth of Closed-Cell Aluminum Foam Sandwich Structures Under Low Velocity Impact
,”
Trans. Jpn. Soc. Artif. Intell. Aerosp. Technol. Japan
,
10
(
28
), pp.
51
58
.
75.
Li
,
Q. M.
,
Magkiriadis
,
I.
, and
Harrigan
,
J. J.
,
2006
, “
Compressive Strain at the Onset of Densification of Cellular Solids
,”
J. Cell. Plast.
,
42
(
5
), pp.
371
392
.
76.
Hallquist
,
J. O.
, and
Whirley
,
R. G.
,
1989
, “
DYNA3D User’s Manual (Nonlinear Dynamic Analysis of Structures in Three Dimensions): Revision 5
,” Lawrence Livermore National Lab., Livermore, CA.
77.
Cowper
,
G. R.
, and
Symonds
,
P. S.
,
1957
, “
Strain-Hardening and Strain-Rate Effects in the Impact Loading of Cantilever Beams
,”
Brown University, Providence
,
RI
.
78.
Yamada
,
H.
,
Hotta
,
M.
,
Kami
,
T.
,
Ogasawara
,
N.
, and
Chen
,
X.
,
2015
, “
Effect of Dynamic Strain Rate on Micro-Indentation Properties of Pure Aluminum
,”
EPJ Web Conf.
,
94
, p.
04034
.
79.
Cherniaev
,
A.
,
2021
, “
Modeling of Hypervelocity Impact on Open Cell Foam Core Sandwich Panels
,”
Int. J. Impact Eng.
,
155
, p.
103901
.
80.
Vengatachalam
,
B.
,
Poh
,
L. H.
,
Liu
,
Z. S.
,
Qin
,
Q. H.
, and
Swaddiwudhipong
,
S.
,
2019
, “
Three Dimensional Modelling of Closed-Cell Aluminium Foams With Predictive Macroscopic Behaviour
,”
Mech. Mater.
,
136
, pp.
103067.1
103067.15
.
81.
Johnson
,
G. R.
, and
Cook
,
W. H.
,
1985
, “
Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures
,”
Eng. Fract. Mech.
,
21
(
1
), pp.
31
48
.
82.
LSTC
,
2007
, “
LS-DYNA Keyword User’s Manual, Version 971
,” Livermore Software Technology Corporation.
83.
Gupta
,
N. K.
,
Iqbal
,
M. A.
, and
Sekhon
,
G. S.
,
2006
, “
Experimental and Numerical Studies on the Behavior of Thin Aluminum Plates Subjected to Impact by Blunt- and Hemispherical-Nosed Projectiles
,”
Int. J. Impact Eng.
,
32
(
12
), pp.
1921
1944
.
84.
Lambert
,
J.
, and
Jonas
,
G.
,
1976
, “
Towards Standardization in Terminal Ballistics Testing: Velocity Representation
,” Army Ballistic Research Lab Aberdeen Proving Ground Md.
85.
Thomson
,
W. T.
,
1955
, “
An Approximate Theory of Armor Penetration
,”
J. Appl. Phys.
,
26
(
1
), pp.
80
82
.
86.
Zhang
,
N.
, and
Yang
,
G.
,
2009
, “
Penetration Analysis of Aluminum Alloy Foam
,”
Engineering Plasticity and Its Applications From Nanoscale to Macroscale
,
Daejcon, South Korea
,
Oct. 20
.
87.
Landkof
,
B.
, and
Goldsmith
,
W.
,
1985
, “
Petalling of Thin, Metallic Plates During Penetration by Cylindro-Conical Projectiles
,”
Int. J. Solids Struct.
,
21
(
3
), pp.
245
266
.
88.
Reid
,
S. R.
, and
Zhou
,
G.
,
2000
,
Impact Behaviour of Fibre-Reinforced Composite Materials and Structures
,
Elsevier
,
New York
.
89.
Fatt
,
M. S. H.
, and
Park
,
K. S.
,
2000
, “
Perforation of Honeycomb Sandwich Plates by Projectiles
,”
Composites Part A
,
31
(
8
), pp.
889
899
.
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